Section 12.10 Applications

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Section 12.10 Applications

• 12.66 A three-phase, four-wire system operating with a 480-V line voltage is shown in Fig. 12.71. The source voltages are balanced. The power absorbed by the resistive wye-connected load is measured by the three-wattmeter method. Calculate:
  • (a) the voltage to neutral
  • (b) the currents I1, I2, I3, and I*ⁿ*
  • (c) the readings of the wattmeters
  • (d) the total power absorbed by the load
• 12.67 As shown in Fig. 12.72, a three-phase four-wire line with a phase voltage of 120 V rms and positive phase sequence supplies a balanced motor load at 260 kVA at 0.85 pf lagging. The motor load is connected to the three main lines marked a, b, and c. In addition, incandescent lamps (unity pf) are connected as follows: 24 kW from line c to the neutral, 15 kW from line b to the neutral, and 9 kW from line c to the neutral.
  • (a) If three wattmeters are arranged to measure the power in each line, calculate the reading of each meter.
  • (b) Find the magnitude of the current in the neutral line.

* An asterisk indicates a challenging problem.

Figure 12.68 For Prob. 12.62.

Figure 12.70 For Prob. 12.65.

• 12.68 Meter readings for a three-phase wye-connected alternator supplying power to a motor indicate that the line voltages are 330 V, the line currents are 8.4 A, and the total line power is 4.5 kW. Find:
  • (a) the load in VA
  • (b) the load pf
  • (c) the phase current
  • (d) the phase voltage
• 12.69 A certain store contains three balanced three-phase loads. The three loads are:

Load 1: 16 kVA at 0.85 pf lagging Load 2: 12 kVA at 0.6 pf lagging Load 3: 8 kW at unity pf

The line voltage at the load is 208 V rms at 60 Hz, and the line impedance is 0.4 + j0.8 Ω. Determine the line current and the complex power delivered to the loads.

Figure 12.72

For Prob. 12.67.

• 12.70 The two-wattmeter method gives P1 = 1200 W and P2 = −400 W for a three-phase motor running on a 240-V line. Assume that the motor load is wye- connected and that it draws a line current of 6 A. Calculate the pf of the motor and its phase impedance.
• 12.71 In Fig. 12.73, two wattmeters are properly connected to the unbalanced load supplied by a balanced source such that Vab = 208⧸ 0° V with positive phase sequence.
  • (a) Determine the reading of each wattmeter.
  • (b) Calculate the total apparent power absorbed by the load.

Figure 12.73 For Prob. 12.71.

• 12.72 If wattmeters W1 and W2 are properly connected respectively between lines a and b and lines b and c to measure the power absorbed by the deltaconnected load in Fig. 12.44, predict their readings.
• 12.73 For the circuit displayed in Fig. 12.74, find the wattmeter readings.

Figure 12.74

For Prob. 12.73.

12.74 Predict the wattmeter readings for the circuit in Fig. 12.75.

Figure 12.75 For Prob. 12.74.

• 12.75 A man has a body resistance of 600 Ω. How much current flows through his ungrounded body:
  • (a) when he touches the terminals of a 12-V autobattery?
  • (b) when he sticks his finger into a 120-V light socket?